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i know the definition by commuting with direct/inverse limits. it can be shown to be equivalent. should this be mentioned? --
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I deleted the second condition for halfexactness, because it was wrong. If a functor fulfills the property, that from A-: -->
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A pedantic point: the first paragraph is a little sloppy, in that it fixes a short exact sequence 0-: -->
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F(C) is exact, then the functor is already exact. Just apply this condition to sequences like 0-: -->
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is left (resp. right) exact if it commutes with finite projective (resp. inductive) limits.
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be a category with finite projective (resp. inductive) limits. Then a functor u from
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be a category with finite projective (resp. inductive) limits. Then a functor u from
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is left (resp. right) exact if it commutes with projective (resp. inductive) limits.
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Short exact sequences redirects to exact sequences. Isn't this a problem?
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ah, i see. its in the examples. i think a more general definition should
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Isn't it necessary that exact functors between abelian categories are
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